Power and Roots (Copy)

1. Write down the value of the following: (4 marks)
a) √144
b) 13²
c) ∛125
d) 4³

2. Recall the square numbers from 1² to 10² and list them. (5 marks)

3. Calculate without a calculator: (3 marks)
a) 2³ × 3²
b) (5²) ÷ (5¹)
c) 10⁰ + 4²

4. Evaluate the following powers: (4 marks)
a) 3⁴
b) 16^(1/2)
c) 1000^(1/3)
d) 2^(-3)

5. State whether these statements are True or False: (4 marks)
a) √81 = 8
b) ∛27 = 3
c) 7² = 49
d) 2^0 = 0

Section B: Structured Questions (Calculator Allowed)

Total Marks: 20

6. Work out the following: (4 marks)
a) 8² + 6³
b) (3²)³

7. Simplify and calculate: (4 marks)
a) 2² × 2³ ÷ 2⁴
b) (4³)^(1/3)

8. A number n satisfies n² = 225.
a) Find n. (1 mark)
b) Verify that n³ = 3375. (2 marks)

9. Evaluate the following expressions: (5 marks)
a) 9^(1/2) + 64^(1/2)
b) 125^(1/3) + 100^(1/2)
c) 2^5 + 3³

10. A machine reduces a value by applying a power of 0:
If the input is 5000, what is the output after applying 5000 × (10⁰)? (2 marks)

1.
a) √144 = 12
b) 13² = 169
c) ∛125 = 5
d) 4³ = 64 (1 mark each)

2. Squares from 1² to 10²:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100 (½ mark each = 5 marks)

3.
a) 2³ × 3² = 8 × 9 = 72
b) 5² ÷ 5¹ = 25 ÷ 5 = 5
c) 10⁰ + 4² = 1 + 16 = 17 (1 mark each)

4.
a) 3⁴ = 81
b) 16^(1/2) = √16 = 4
c) 1000^(1/3) = ∛1000 = 10
d) 2^(-3) = 1 / 2³ = 1/8 (1 mark each)

5.
a) False (√81 = 9)
b) True
c) True
d) False (2⁰ = 1) (1 mark each)

6.
a) 8² + 6³ = 64 + 216 = 280
b) (3²)³ = 9³ = 729 (2 marks each)

7.
a) 2² × 2³ ÷ 2⁴ = 2^(2+3−4) = 2¹ = 2
b) (4³)^(1/3) = 4^(3×1/3) = 4¹ = 4 (2 marks each)

8.
a) n² = 225 → n = 15 (1 mark)
b) n³ = 15³ = 3375 ✓ (2 marks)

9.
a) 9^(1/2) + 64^(1/2) = 3 + 8 = 11
b) 125^(1/3) + 100^(1/2) = 5 + 10 = 15
c) 2⁵ + 3³ = 32 + 27 = 59 (1 mark each, total 5 marks)

10.
5000 × (10⁰) = 5000 × 1 = 5000 (2 marks)